There are some techniques which allow one to interpolate between the spaces.
Two methods, the "\(K\) -method" and the "\(J\) -method," can be
used to interpolate between \(L^2(U)\)  and \(W^1(U)\) , each
with equivalent norms. We refer the reader to [1]} for
a description of these methods.
From Theorem 15.1 in [2]}
the spaces \(W^{\epsilon }(U)\)  as defined above are equivalent to
those produced by using
interpolation via the \(K\) -method, and give equivalent norms. Furthermore,
we can use a norm described as in [1]} to calculate the \(K\) -method
norms.
To calculate the \(W^{\epsilon }\) -norm (\(0<\epsilon <1\) ) of a function,
\(f\) , known to be in \(W^1(U)\) , we will use that
\(\Vert f\Vert _{W^{\epsilon }(U)}\)  is
comparable to the infimum of the norm
\(I(u)=\\\left( \int _0^{\infty }\left\Vert  t^{1-\epsilon } u(t)\right\Vert ^2_{W^1(X)} t^{-1}dt\right)^{1/2} + \left(\int _0^{\infty }\left\Vert  t^{1-\epsilon } u^{\prime }(t)\right\Vert ^2_{L^2(X)} t^{-1}dt\right)^{1/2}\) 
